0
$\begingroup$

After finishing a chapter on Rank-Nullity in linear algebra I came across the following problem:

Suppose that $M,N$, are subspaces of a finite-dimensional vector space $V$ such that the dimensions of

$(M+N)/N = 2$,

$(M+N)/M = 3$,

$(M \cap N) = 4$

Then what are the dimensions of $N$, $M$, and $M+N$.

Thoughts:

$\dim (M+N)/N = \dim (M+N) - \dim (N) = 2$, and

$\dim (M+N)/M = \dim (M+N) - \dim (M) = 3$, Thus $\dim (N) - \dim(M) = 1 $ . This is where I am stuck. Hints appreciated.

$\endgroup$
1
$\begingroup$

Use the formula for the sum of two vector spaces.

For reference, it is in the question of this: Dimension of the sum of two vector subspaces

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.